ISSN:
1572-9532
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract Let (M, g) be a Lorentzian warped product space-timeM=(a, b)×H, g = −dt 2 ⊕fh, where −∞⩽a〈b⩽+∞, (H, h) is a Riemannian manifold andf: (a, b)→(0, ∞) is a smooth function. We show that ifa〉−∞ and (H, h) is homogeneous, then the past incompleteness of every timelike geodesic of (M,g) is stable under smallC 0 perturbations in the space Lor(M) of Lorentzian metrics forM. Also we show that if (H,h) is isotropic and (M,g) contains a past-inextendible, past-incomplete null geodesic, then the past incompleteness of all null geodesics is stable under smallC 1 perturbations in Lor(M). Given either the isotropy or homogeneity of the Riemannian factor, the background space-time (M,g) is globally hyperbolic. The results of this paper, in particular, answer a question raised by D. Lerner for big bang Robertson-Walker cosmological models affirmatively.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00758551
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